ON THE POSSIBILITY OF LIQUID-LIKE STATE IN THE GRAIN BOUNDARY REGIONS OF POLYCRYSTALS

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ON THE POSSIBILITY OF LIQUID-LIKE STATE IN THE GRAIN BOUNDARY REGIONS OF

POLYCRYSTALS

Yu. Nechaev

To cite this version:

Yu. Nechaev. ON THE POSSIBILITY OF LIQUID-LIKE STATE IN THE GRAIN BOUNDARY REGIONS OF POLYCRYSTALS. Journal de Physique Colloques, 1990, 51 (C1), pp.C1-287-C1-292.

�10.1051/jphyscol:1990145�. �jpa-00230304�

COLLOQUE DE PHYSIQUE

Colloque Cl, supplBment au nol, Tome 51, janvier 1990

ON THE POSSIBILITY OF LIQUID-LIKE STATE IN THE GRAIN BOUNDARY REGIONS OF POLYCRYSTALS

Moscow Institute o f Steel and Alloys, 4 Leninsky Prospect, 117936, U.R.S.S.

R e s d

-

A la base de lqexamen thermodynamique et cingtique, en utilisant les donn6s des Btudes blectroniques et microscopiques de la structure disloqu6e , on a montr6 la possibilit6 de la formation dans les mktaux, notamment dans les domaines des limites des grains, de l q 8 t a t liquide A la deformation superplastique ou au recuit des 6chantillons d6form6s. On a fait les Bvaluations pour l'alliage de magn6sium (Mg + 1,5% Mn + 0,3% Ce), la dimension des grains &ant prbs de 10 pm, pour l'acier inoxydable austenoferritique ( m 10 pm) et pour les polycristaux de nickel ( W 0 , s pm),

Abstract

-

The p o s s i b i l i t y of t h e l i q u i d - l i k e s t a t e formation i n me- ' t a l s i n t h e g r a i n boundary regions under s u p e r p l a s t i c deformation or

annealing of deformed specimens has been shown basing on thermodynamic and k i n e t i c consideration with t h e use of electron-microscopic d a t a on a d i s l o c a t i o n s t r u c t u r e . Magnesium a l l o y (Mg

+

I

.5%

Mn

+

0.3% Ce) with

I0 urn g r a i n s i z e , f e r r i t e - a u s t e n i t e s t a i n l e s s s t e e l ( I 0 um) and nick& p o l y c r y s t a l a ( 4 0.5/um) have been considered. /

According t o a concept of /I,2/ t h e phenomenon of s t r u c t u r e s u p e r p l a s t i c i t y (SSP) of metals i s r e l a t e d t o t h e g r a i n boundary (GB) t r a n s i t i o n i n t o n l i q u - id-like" s t a t e when t h e GB a r e "bombarded" by l a t t i c e d i s l o c a t i o n s (LD).

Within t h e framework of models /I,2/ t h e formation of t h i s s t a t e i s caused by a d e s t a b i l i z a t i o n of GB s t r u c t u r e due t o continuous d e l o c a l i z a t i o n pro- c e s s e s of t h e LD cores in boundaries. Qe see from paper /2/ t h a t t h e use of term "liquid-like" high-activated s t a t e i n models / I , 2 / shows t h a t t h e GB

s t r u c t u r e under SSP conditions i s unstable t o a shear deformation and has an anomalously high i n t e n s i t y of t h e atomic re-arrangement of s t r u c t u r e . As i s supposed from paper /3/ a s i g n i f i c a n t decrease of t h e deformation r e - s i s t e n c e under SSP a r i s e s from a "pseudo-liquidtt s t a t e s t r u c t u r e o r " a e t i - v a t e d atom complexes" formed i n m a t e r i a l due t o a su e r s a t u r a t i o n with l a t - t i c e d e f e c t s and t h e development of heterophase flucguations. Close term

t'quasiliquid boundary" i s used i n works /4/ f o r describing t h e i n t e r g r a n u l a r boundary s t a t e s under " s u p e r p l a s t i c i t y of transformation".

According t o a concept of /5-8/ t h e pain-boundar s l i p and boundary migra- t i o n under SSP a r e r e l a t e d wiith t h e m c r e a s e of G% nonequilibrium (when they absorb t h e LD) and subsequen* development of CB s t r u c t u r e recovery. I n paper /8/ t h e term

"

nonequilibrium f i r s t - t y p e s t a t e t 1 i s used f o r t h e GB with a high c o n c e ~ t r a t i o n of "absorbed" LD, and t h e term ttnonequilibrium second-type s t a t e

-

f o r t h e GB i n which t h e s t r u c t u r e recovery determining

"jump-wise" modification of t h e k i n e t i c s of d i f f u s i o n and deformation prope- r t i e s t a k e s place. The a u t h o r s of paper /8/ po'int t o t h e grain-boundary

s t r u c t u r e transformation (while absorbing t h e LD) from t h e first- ( I ) t o t h e second-type s t a t e (I1 ), metastable or nonst ationary under c e r t a i n condi- t i o n s . They assume /6-8/ t h a t nonequilibrium GB s t a t e I1 during SSP i s caus- ed by LD d i s s o c i a t i o n absorbed by boundaries on t h e " d i s c r e t e introduced grain-boundary d i s l o c a t i o n s " with t h e small Burgers v e c t o r s and high mobi-

(I) Pcesent addre ss : The Pilot-Plant a t t h e Karaganda Metallurgical iYorks, W Lenin S t r e e t , Temirtau, 472300 Karaganda Region, USSR

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990145

Cl-288 COLLOQUE DE PHYSIQUE

liw;

c r i t i c a l n o t e s a r e formulated i n paper / W .

I n t h e l i g h t of model / I , 2 / t h e GB t r a n s i t i o n from s t a t e I t o s t a t e I1 cor- responds t o t r a n s i t i o n from the c r y s t a l l i n e GB s t r u c t u r e with high density of t h e absorbed LD t o " l i q u i d - l i k e u GB s t a t e , i.e. t o a s p e c i f i c phase t r a - n s i t i 0 n . A ~ was mentioned i n /I/ the p o s s i b i l i t y of t h i s t r a n s i t i o n i n GB r e - gions i s i n d i c a t e d by a jump-wise change of the d i f f u s i o n and deformation p r o p e r t i e s of boundarie ^S.

According t o experimental d a t a of any guth r s the G B s a t u r a t i o n l i m i t with absorbed IID f o r some metals i s IOjm- I 0 m/m% (electcon-microscopic /8/ and c a l o r i m e t r i c d a t a / 5 / ) t h a t , evidently, corresponds t o s t a t e I. This s t a t e can be reached under s m a l l degrees of p l a s t i c deformation of specimens a t low temperatures /8/. Subsequent annealing of specimens under c e r t a i n con- d i t i o n s l e a d s t o a ''spreading" and disappearance of e l e c tron-micro scopic images of the LD absorbed by boundaries /6-10/ and the development of "non- equilibrium GB p r o p e r t i e s u corresponding t o s t a t e I1 i n deformation and r e - c r y s t a l l i z a t i o n processes /7,8/. The time r e q u i r e d f o r a disappearance of e l e c t r o n microscopic disl c a t i o n images i n GB r e g i o n s corresponds apparently t o c h a r a c t e r i s t i c time (

PI

⁾ of transformation of GB s t r u c t u r e from s t a t e

I

t o s t a t e I1 a t the temperature of experiment. Thus, f o r random high angle g r a i n boundaries,

7

I -11 f o r magnesium at room temperature i s I- I 0 hours, and f o r the MA 8 a l l o y (Mg

+

I .5% Mn

+

0.3% Ce) a t 670 K

-

of t h e or- der of a few seconds /6,7/. For random high angle g r a i n boundaries i n ^{N i}

,

N i

+

5% XL a u s t e n i t e s t e e l and a l l o y (Al

+

O.% Mg) a t high temperatures (0.3

-

0.5) Tm, where Tm i s t h e c r y s t a l melting p o i n t , I-II i s 10- I00 sec /9,IO/. The experimentd data /7,8/ of ^the manifestation of nonequ- i l i b r i u m GB p r o p e r t i e s i n s t a t e I1 i n deformation and r e c r y s t a l l i z a t i o n pro.

c e s s e s and those on annealing regimes of none u i l i b r i u m GB / I O / have t h e i n - formation on a c h a r a c t e r i s t i c time (

II-oj(

^{of GB} s t r u c t u r e transformati- on from s t a t e I1 i n t o c r y s t a l s t a t e ( 0 ) wxth a r e l a t i v e l y low d i s l o c a t i o n density.

Due t o already s a i d , using t h e experimental r e s u l t s of /5-10/ i t i s worth considering w i t h i n t h e framework of thermodynamics and formal k i n e t i c s the p o s s i b i l i t y o f t h e i n t e r p r e t a t i o n of s t a t e I1 in GB regions of metals under SSP or annealing t h e cold-deformed specimens l i k e l i q u i d - l i k e (without i n - v e r t e d commas), i .e

.

t h e p o s s i b i l i t y of temporary GB "softening" because of decrease of t h e melting point of t h e nonequilibrium GB s t r u c t u r e ( s t a t e I ) up t o deformation o r annealing temperature.

I n view of thermodynamics t h e c r y s t a l l i n e GB s t r u c t u r e with high d i s l o c a t i o n density ( s t a t e I ) can be i n equilibrium with t h e l i q u i d - l i k e GB s t r u c t u r e

(presumable s t a t e 1 1 ) a t t h e annealing temperature Ta i f the change of Gibbs energy f o r 1-11 i n the u n i t volume of GB regions i s equal t o zero, i.e.

A GIhII(Ta) = GII(Ta)

-

^{GI(Ta) = 0}

Such a s i t u a t i o n can be v a l i d i f i n s t a t e I t h e d i s l o c a t i o n ener y "stored"

i n t h e u n i t volume of GB r e g i o n s a t low-temperature deformation ? A Go --I

1

i s closed t o t h e change o f Gibbs energy ( A Gm) a t t h e f u s i o n of t h e u n i t volume of s t r u c t u r e "0" a t T a :

where ⁴ Hm i s the s p e c i f i c f u s i o n enthalpy of metal ^(0); Tm i s the melting o i n t of s t r u c t u r e "O", d i s t h e metal density (0). The ~ ~ ~ s t a l l i z a t i o n

?II--0) of the u n i t volume of GB r e g i o n s a t Ta i s characterized by the

change of Gibbs energy

It follows from e q s . ( I ) and ( 3 ) t h a t _{A GI} -I==

-

^A GII-O-AGO-I= 0 , i.e. Ta can be melting p o i n t f o r t h e GB r e g i o n s with s t r u c t u r e I.

A k i n e t i c condition f o r t h e l i q u i d - l i k e GB s t a t e (IS) while annealing t h e cold-deformed specimens a t Ta i s revealed i n low c h a r a c t e r i s t i c time of the process 1-11

(f

I ) a s compared with t h e c h a r a c t e r i s t i c times of ot- her processes (

2

11 ,0,

F

I,O). T h i s condition can be s a t i s f i e d . Accord- i n g t o aforementioned experimental data /8/ a f t e r "spreading" e l e c tron-&c- roscopic images of t h e LD absorbed by boundaries (i.e. a f t e r t h e process of 1-11) the g r a i n boundaries (11) e x h i b i t over a c e r t a i n time (of t h e order of II--t O ) t h e nonequilibrium p r o p e r t i e s i n the deformation and r e c r y s t a - l l i z a t i o n processes.

There a r e some grounds t o assume t h a t under s u p e r p l a s t i c deformation of me- t a l s i n t h e GB regions a c y c l i c process of t r a n s i t i o n of t h e deformation work i n t o heat can take place and has t h e following s t a g e s : I ) transformati- on of c r y s t a l s t r u c t u r e "0" i n t o c r y s t a l s t r u c t u r e I equilibrium with l i q u i d - l i k e s t a t e (11) a t t h e deformation temperature TE ; 2 ) t r a n s i t i o n 1-11

a t ^Tt = const [fusioq); 3 ) t r a n s i t i o n 11-0 a t t h e temperature c l o s e t o T t (with the d i s s i p a t i o n of c r y s t ; a l l i z a t i o n heat )

.

The s t a t i o n a r y condition of this cycle i n GB regions under SSP i s t h a t t h e r a t e s of t h e separate s t a g e running a r e equal. The c h a r a c t e r i s t i c times of t h e separate s t a e s should be obviously lower t h a n t h e general time of de- formation ( t C

$.

Considering i n t h e i l l u s t r a t i v e plan t h e f i r s t - o r d e r three"seactiontl cycle t h e s t a t i o n a r y condition can be represented a s :

where CO, CI and CII a r e t h e corresponding llconcentrations". From t h i s equ- a t i o n it follows t h a t s t a t e I1 considerable develops a t t h e s t a t i o n a r y pro- c e s s i f condition

i s s a t i s f i e d . I n t h e l i m i t of t h i s concept a s t a t i o n a r y r a t e of t h e forma- t i o n of s t a t e I i s described i n t h e following way:

where CI c T/D i s t h e volume f r a c t i o n of GB r z g i o n s ; D i s t h e g r a i n dia- meter i n p o l y c r y s t a l s , dGI/dt r

4 2 6

^{/d Gm ;}

E

i s t h e deformation r a t e ;

d

i s t h e s t r e s s ; 4 I ; A G i s t h e change of Gibbs e n e r m in f u s i o n of t h e volume u n i t of c r y s t a l ( o ) ~ a t

TI .

Using eqs. ( 2 ) an& (5) we o b t a i n the expression f o r a f r a c t i o n of deformation power expending on s t a t e I :

Cl-290 COLLOQUE DE PHYSIQUE

The s t a t i o n a r y "bulk" density of dislocations ( F I ) i n GB regions (I) can be estimated by equation (5) assuming t h a t CI c I!/D and dCI/dt ^t

= d t b / @

b h ) ; pl i s t h e shear modulus of m a t e r i a l (O), b i s t h e Bur- g e r s vector magnitude. Whence, we o b t a i n t h a t

where fI * i s t h e s t a t i o n a r y "surface" density o f d i s l o c a t i o n s i n GB r e g i o n s ( 1

1

From eqs. ( 6 ) and ( 7 ) it follows t h a t

_PI

.c const at given Tc :

I n o t h e r words, s t a t e I equilibrium with s t a t e I1 a t TE i s r e a l i s e d while a t t a i n i n g t h e d i s l o c a t i o n density QI i n GB regions.

For estimating

PT

* one can use t h e well-known expression from d i s l o c a t i o n theory : &/dt c /2,5,6/. In eq. ( 5 ) we can assume then

C, ^C

P;/(

^p1D) and dCI/dt r ($@=D) dp;/dt; from which we o b t a i n

P; e irI-IIb

From eqs.(7>, (8) and ( 9 ) i t follows

One can a l s o assume t h a t i n p01 c r y s t a l s under SSP a concentration of t h e g r a i n i n t e r i o r vacancies g r aduafly i n c r e a s e s up t o t h e value corresponding t o equilibrium with l i q u i d s t a t e I1 i n t h e GB regions. A comparative incre- a s of t h e concentration of t h e g r a i n i n t e r i o r vacancies can be a s follows:

where M. i s t h e molar mass of metal; R js the universa12gas constant. The r e l a x a t i o n time o f t h e process i s determined a s D / DV

,

^{where DV}

i s t h e d i f f u s i o n c o e f f i c i e n t of t h e vacancies i n c r y s t a l ( 0 ) a t Tq

.

The problem of t h e vacancies flows and t h e impurity atom r e d i s t r l b u t ; i o n between t h e g r a i n volumes and GB regions c a l l s ' f o r a separate consideration.

For t h e i l l u s t r a t i v e e s t i m a t e s one can use t h e SSP experimental d a t a /6,7/

f o r MA8 a l l o y closed by a s t r u c t u r e t o uni-phase a l l o y S. The optimum tempe- r a t u r e - r a t e regime o f s u p e r p l a s t i c deformation of MA8 a l l o y has t h e follow- i n g parameter s /6,7/ : !lc = 673 K, d r - 2 5 W a , D = IO,u.n,

2

1,11=1 S,

,$=I.

10'~s". By s u b s t i t u t i n g these q u a n t i t i e s into eqs. (8)-(11) a n d using t h e Table v a l u e s A

%,

^,P,! d , JI and b we o b t a i n l h 1.10-%( (&%cqrcI&?ce

16 3 7 2 (Sn

#atbe autoionic microscopy d a t a ) , J I r 4.10 m/m

, P;=

4.10 m/m accor- d a n s h r experimental values

P*

/6/ ) ; d - IO-~. Using eq.(12) we o b t a i n t h a t D GV/CV e 0.2 and TV i s of t h e order of 1-10 S. The corresponding

e s t i m a t e s shows a l s o t h a t while proceeding t h e s t a g e s of c y c l e t h e l o c a l -

-

mperature increase i n GB r e g i o n s i s n e l i g i b l y small. The low value ⁴ = I 0

Se

i s l i k e l y r e s u l t s from the r e v e r s e process@ -+I), l e a d i n g t o energy d i s s i - pation,

Using t h e SSP experimental data /II,q,IO/ f o r f e r r i t e - a u s t e n i t e s t a i n l e s s

r

_{- I S}

s t e e l ⁽ TE = 1233 K , =

I . I o - ~ s - ~ , d

= 63 MPa, D = LO/um, L I,11- one can o b t a i n the analogous r e s u l t s :

Experimental r e s u l t s /12,13/ on a nonmonotonic change of mechanical and phy- s i c a l p r o p e r t i e s of p o l y c r y s t a l l i n e n i c k e l under low-temperature deformation confirm t h e p o s s i b i l i t y of t h e c y c l i c process "nonequilibrium boundary melt- i n g

-

c r y s t a l l i z a t i o n " . W can assume t h a t t h e low-temperature deformation e of metals can l e a d t o a s i t u a t i o n when t h e c h a r a c t e r i s t i c times of t h e se-;

p a r a t e s t a g e s of t h e c y c l e s u f f i c i e n t l y exceed t h e deformation time

(AL

/E

,

where 4 t i s t h e deformation i n t e r v a l between measurements). A k i y t i c s of t h e separate stage of cycle can a l s o be measured i n t h i s case. Such a s i t u - a t i o n appears t o occur under t h e r o l l i n g of n i c k e l a t room temperature

b f

= 0.02

-

0.05), where t h e r e observes a r e p e t i t i v e jump-wise d e v i a t i o n from monotonic change of deformation p r o p e r t i e s

/Ia/

and t h e d e f e c t component of s p e c i f i c e l e c t r i c a l r e s i s t a n c e of metal /I2/, Fig .I.

A n a n a l y s i s of r e s i s t o m e t r i c and electron-microscopic d a t a /12/ on isochro- n i c (Fig .2) and isothermal annealing of t h e dcf ormed specimens showed t h a t the li@al cgncentration of d i s l o c a t i o n s i n t h e subgrain boundary regions i s I 0 m/m (with t h e s u b p a i n s i z e

-

0.5 pm). Under c e r t a i n degrees of deformation (

E ,

⁾ t h e l o c a l density of d i s l b c a t i o n in t h e subgrain bounda- r y r e ions i s jump-wise changed (up to-%; according t o r e s i s t o m e t r i c d a t a , p i g .I? ; i n t e r g r a n u l a r d i s l o c a t i o n densxty remains n e g l i g i b l y small ( e l e c t - ron-microscopio data). A t t h e c l o s e v a l u e s o f c c t h e nonotonic change of p l a s t i c deformation r e s i s t a n c e , p l a s t i c i t y , hardness and other c h a r a c t e r i s - t i c s of the deformed metal was destroyed

/m/.

Thus, a t

e c

⁼ 0.55

-

0.60 t h e r e was observed a s i g n i f i c a n t decrease (up t o 10%) of hardness

of deformed N i specimens /U/ corresponding t o a sharp i n c r e a s e of t h e de-

f e c t component of e l e c t r i c a l r e s i s t a n c e (Fig.1) /IW.

Fig. I

-

Dependence of t h e "defect" component of s p e c i f i c e l e c t r i c a l r e s i s - tance of n i c k e l

(PP)

on t h e degree of p l a s t i c a l deformation of specimens;

r o l l i n g a t 295 K.

Fig. 2

-

Cha.nge of t h e "defect" component of s p e c i f i c e l e c t r i c a l r e s i s t w c e of t h e deformed specimens of N i (

bp

) under isochronic annealing

(

'L-

= 7 min); curve I

-

E ⁼ 0.59; curve 2

-

& ⁼ 0.61.

Cl-292 COLLOQUE DE PHYSIQUE

Paper

/Ia/

r e p o r t s on t h e conclusion where t h e r e s u l t s point t o a r e a l pos- s i b i l i t y of t h e r e p e t i t i v e phase t r a n s i t i o n s i n subgrain boundary r e g i o n s from high d i s l o c a t i o n d e n s i t y c r y s t a l s t a t e ( I ) t o l i q u i d - l i k e (amorphous) s t a t e 11. The time e x t e n t of phase t r a n s i t i o n s i s obviously r e l a t e d t o the correspondin averaging over t h e d e f e c t regions. It i s shown i n paper /IS/

t h a t nonmonofonic strengthening of metal (NI) under low-temperature ceforma- t i o n can a r i s e from r o t a t i o n a l i n s t a b i l i t i e s and c o l l e c t i v e b s l o c a t l o n en- semble modes determining t h e local. change of t h e d e f e c t s t r u c t u r e on t h e type of phase t r a n s i t i o n .

A c o n s i d e r a t i o n of t h e p r e s e n t paper shows t h a t t h e GB regions can be "sof- tened" i n deformed metal due t o decrease of t h e melting p o i n t of nonequilib- rium boundary s t r u c t u r e ( I ) up t o deformation and annealing temperature.

The mechanisms of phase t r a n s i t i o n s ( I-+I1 and 1 1 - 4 0 ) can be considered and a physical sense of high experimental v a l u e s

Tl:

-11 andTII-o can be r e v e a l e d on t h e b a s i s of t h e d i s l o c a t i o n mechanism of c r y s t a l melting /I4/ i n c l u d i n g t h e 2D case /IS/. I n t h e p r e s e n t c o n s i d e r a t i o n t h e e f f e c t i v e c h a r a c t e r i s t i c s of I and

T

have an i l l u s t r a t i v e - e m p i r i c a l sense.

Nevertheless, at present our experiments are at a macroscopic scale and there is evidence supporting the above described model is quite indirect. It would be useful to investigate the structure of the deformed material at the interfaces with HREM in order to coroborate our assumptions.

Moreover, equilibrium thermodynamics has been used , although the dynamical behavior of the experimental system may do not be satisfactority represented in such a framework. Future work will be devoted to the investigation of the thermodynamical properties far from equilibrium and to possible dynamical effects which will require the present thermodynamic description to be improved.

/I/ Perevezentsev, V.N., Rybin, V.V., Orlov, A.N. Poverkhnost

, ⁶

⁽¹⁹⁸²⁾

134-142, ( i n Russian).

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